# Isotopes

### Isotopes

#### Lessons

In this lesson, we will learn:
• The definition of an isotope and their difference in properties.
• The definition of relative atomic mass and relative isotopic mass
• How isotopes come to affect the relative atomic mass of an element.
• How to calculate relative mass of samples using relative abundance.

Notes:
• So far, we have ignored the fact that many elements in the Periodic Table have decimal numbers in their relative atomic mass.
• If atomic mass is a measure of the number of protons and neutrons in an atom, how is it possible to have atomic mass that isn't a whole number? Remember, you cannot have half a proton or half a neutron in an atom!

• The reason that relative atomic masses sometimes contain decimals is because they are averages accounting for different isotopes of each element.

• An isotope is an atom of an element with the same number of protons but a different number of neutrons. This gives an equal proton number (so by definition it's the same element) but a different mass number.

• “Relative” when talking about the mass of any atom or molecule, means relative to carbon-12. The mass of any isotope or atomic sample is defined as compared to the carbon-12 (12C) isotope:
• The relative isotopic mass is the mass of an isotope relative to 1/12 of the mass of a 12C atom.
• The relative atomic mass is the mass of any atomic sample relative to 1/12 of the mass of a 12C atom.

• Any given element (defined by the proton number!) might have atoms with different numbers of neutrons. This element's range of atoms with different numbers of neutrons in them are its' isotopes.
• For example, hydrogen atoms have only 1 proton, and can only have one proton.
• Hydrogen atoms with zero neutrons are called Hydrogen-1. This is by far the most common isotope of hydrogen we observe. About 99.98% of hydrogen atoms are hydrogen-1.
• Hydrogen atoms with one neutron are called Hydrogen-2 or deuterium. This only makes up about 0.02% of any sample of hydrogen atoms.
• Another example: Carbon atoms have 6 protons in their nucleus and can only have 6 protons.
• The most common isotope of carbon atoms is carbon-12, which has 6 protons and 6 neutrons in the nucleus. Around 98.9% of carbon atoms in any sample are carbon-12.
• Carbon-13 is an isotope of carbon where the carbon atoms have 6 protons and 7 neutrons in the nucleus.
• Isotopes are normally specified by giving their relative atomic mass: e.g. carbon-13, or hydrogen-2.

• Because neutrons have no charge, the number of neutrons doesn't change an atom's chemical reactivity. Therefore isotopes of an element have identical chemical properties to each other isotope!

• Because neutrons have a relative atomic mass of 1 amu (the same as protons), isotopes do affect the relative atomic mass of elements as they are written in the periodic table. Ice cubes made of normal water are less dense than liquid water. Ice cubes made with deuterated water, where the hydrogen atoms are hydrogen-2 atoms, sink in liquid water!

• It is possible to calculate molar mass of an elemental sample when given relative abundance of each isotope and individual masses. Multiply the mass of each individual isotope by its percentage abundance, then add these values for each isotope together for the relative molar mass of the elemental sample. In the same way, an isotope's relative abundance can be found if the relative mass is known and the other isotope abundances are too.
• Introduction
Introduction to isotopes
a)
What is an isotope?

b)
Why does Cl have atomic mass of 35.5?

c)
Definition of relative atomic mass and relative isotopic mass.

d)
Using relative abundance to calculate molar mass of elements.

• 1.
Use the number of particles to identify elements, and use elements to determine number of particles.
Complete the table below. When writing the chemical symbol, write the mass number, and charge on the particle with it.

• 2.
Calculate relative mass of elements using relative abundance of their isotopes.
Use the data on relative abundance of the following isotopes to find the molar mass of a sample of these elements.
a)
$^{84}$Sr 0.56%$, ^{86}$Sr 9.86%$, ^{87}$Sr 7%$, ^{88}$Sr 82.58%

b)
i) $^{107}$Ag 51.84%$, ^{109}$Ag 48.16%
ii) $^{35}$Cl 76%$, ^{37}$Cl 24%